Transient Analysis of Age-MRSPNs by the
Method of Supplementary Variables

Miklós Telek, András Horváth

Abstract:

In order to assist the performance evaluation of complex
stochastic models, automatic program tools were developed
since a long time. Stochastic Petri Nets (SPN) are
applied as an effective model description language supported
by several analytical and simulation tools. The analytical
description and the numerical analysis of non-Markovian
stochastic Petri Net models gained attention recently.
There are different theoretical approaches and numerical
methods considered in recent works, such as the Markov
renewal theory and the supplementary variable approach, but
to find the most effective way of the analysis of such
models is still an open research problem.

The supplementary variable approach was successfully applied
to the transient and steady state analysis of Markov
Regenerative Stochastic Petri Nets (MSRPN) when the
preemption policy associated with the Petri Net (PN)
transitions was preemptive repeat different (prd), but it was not applicable with other preemption
mechanisms. In this paper we extend the applicability of
the supplementary variable approach to a class of MRSPNs in which preemptive resume (prs) policy
can also be assigned to the transitions of the PN.